Capacitive resolver



Aug. 9, 1966 B. P. BLASINGAME CAPACITIVE RESOLVER 2 Sheets-Sheet 1Original Filed Nov. 8, 1959 AMPLIFIER %%zu ATTORNE'Y 1966 B. P.BLASINGAME 3,265,960

CAPACITIVE RESOLVER Original Filed Oct. 8, 1959 2 Sheets-Sheet 2 5 MZgfi ATTORNEY United States Patent 3,265,960 CAPACITIVE RESGLVERBenjamin P. Blasingame, 2621 E. Menlo Blvd. Milwaukee, Wis.

Original application Oct. 8, 1959, Ser. No. 845,242, now Patent No.3,172,023, dated Mar. 2, 1965. Divided and this applicatiouOct. 16,1964, Ser. No. 404,379

4 Claims. (Cl. 323-128) This is a division of my copending applicationSerial No. 845,242, filed October 8, 1959, now Patent No. 3,172,023.

This invention relates to resolvers and, more particularly, to acapacitive resolver for providing electrical signals which are relatedin phase to the relative angula disposition of two members.

Present day resolvers are electromechanical devices which provide analternating current signal voltage Whose phase differs from that of areference voltage by an amount precisely equal -to the shaft rotation ofthe resolver. This action is accomplished by means of a four pole statorcontaining two field windings excited by voltages which are precisely 90out of electrical phase with respect to each other inside of which a twopole armature containing a single winding is rotated by the resolvershaft. This field arrangement is essentially analogous to that of a twophase induction motor wherein field windings are excited 90 out ofelectrical phase to produce a rotating magnetic field. The singlearmature winding of the resolver acts like the secondary of atransformer having induced in it the sum of voltages from both fieldwindings. The voltage induced by each field winding is proportional tothe sine of the angle between the axis of the armature and the axis ofthe field pole. Thus the armature voltage is given by the mathematicalexpression:

Where e armature voltage magnitude n =turns ratio of armature to polenumber 1 e =voltage magnitude impressed on field number 1 w=frequency ofexcitation voltage in radians/sec t=time in seconds x=angle between axisof armature winding and field pole number 1 n =turns ratio of armatureto pole number 2 e =voltage magnitude impressed on field number 2 Sincethe armature is rigidly fastened to the resolver shaft, or is also theangle of the resolver shaft with respect to the reference position.

This may be rewritten:

If now n is made equal to n by manufacture and e is made equal to e bythe excitation provisions, then applying the formula cos (x+y)=cos x cosysin x sin y This may be rewritten:

e =ne cos (wH-oc) angle can thus be made to rotate through 360electrical degrees for some fraction of a complete rotation of theshaft. This introduces an ambiguity in the actual shaft position whichmust be accounted for by some means such as another single speedresolver. Such applications are common in the present instrumentationart.

Twoproblems in the use of resolvers are the inaccuracy, backlash andexpense introduced by gearing resolvers for high accuracy and theelectrical and mechanical problems attending the use of slip rings andbrushes to connect the armature windings to the resolver terminals. Theformer problem limits the accuracy of such systems to the accuracy ofgear'trains and the latter limits the applications to environments whichare relatively free of vibration, corrosion, etc.

According to the present invention, a resolver is provided which willproduce an output voltage, the electrical phase angle of which isrelated to the position of a rotatable member by some integral multiplewithout the use of auxiliary gearing and its attendant inaccurary, costand inconvenience. In general, this is accomplished by means of acapacitive resolver including a stator member and a rotor member, one ofwhich members includes at least four capacitive elements which aresymmetrically disposed about an axis, and the other of which membersincludes a single element which is rotatable over the other elements.The single element is axially spaced from the four elements and iscapacitively associated therewith. To provide the signals in accordancewith the invention, a first time varying voltage is impressed across onediagonally opposite pair of the four elements, and a second time varyingvoltage which is in quadrature with the first voltage is impressedacross the other diagonally opposite pair of elements. The singleelement is of such a configuration as to face or be capacitivelyassociated with a single one of the four elements when the stator androtor members are in a reference position and to overlap two of the fourelements when the stator and rotor members are relatively rotated fromthe reference position. According to this scheme, a voltage is impressedupon the single element which has a phase angle with respect to thefirst voltage related to the angle of displacement of the rotor andstator members.

In accordance with a preferred form of this invention, the design of theindividual capacitor elements or plates is such that the set of four or4n plates may be disposed in a single plane on the stator member therebypermitting a single plane rotor plate so that the inventive resolver isespecially compact and of simple mechanical design. According to aparticular embodiment of the invention, a set of four or 4n conductiveplates may be coplanarly disposed in circular symmetry on the statormember and a single conductive plate which is axially spaced from thestator plates may be provided on the rotor member. The rotor and statorplates may be shaped to correspond to certain specified mathematicalcurves thereby to provide a capacity between the stator and rotor whichis propor-' tional to the sine of the angle of displacement between therotor and stator members as measured from a reference position.

In addition, according to a further embodiment of the invention, thedesign of the rotor and stator plates may be made in a multi-leafedpattern according to a certain mathematical formula to provide anydesired multiple speed effect. Accordingly, extremely high accuracy andsenstivity may be achieved from the invention without the use of step-upgearing.

Other objects and structural details of this invention will be apparentfrom the following description when read in connection with theaccompanying figures wherein:

FIGURE 1a and 1b are illustrative of the design of the rotor and statorplates in accordance with a specific embodiment of the invention and areused in establishing the methematical nomenclature in the specificationfollowing;

FIGURE 2 is a schematic circuit diagram indicating how capacitors formedin accordance with the plate configurations of FIGURES l and 1a may beused with a preamplifier to provide a voltage proportional to capacity;

FIGURE 3 is a plan view of the rotor and stator plate con gurations of asingle speed capacitive resolver in accordance with a specificembodiment of the invention;

FIGURE 4 is a duplication of FIGURE 3 with the rotor plate angularlydisplaced to an arbitary position;

FIGURE 5a is a plan view of a two-speed capacitive resolver inaccordance with a specific embodiment of the present invention; and

FIGURE 5 b is a view of the two-speed capactive resolver rotor.

Referring first to FIGURE la, it is seen that asingle stator plate isshown by a dotted outline while an associated rotor plate 12 shown .by asolid line has been turned from the reference position through the angleon so the area marked by cross hatching is common to both the stator andthe rotor. This area of overlap forms a capacitor. It is to be noticedthat only a single stator plate is shown; in the complete resolverinstrument, a minimum of [four such plates are necessary. The peripheryof both the stator and the rotor plates are circles of radius R andcenter at the center of rotation marked by the cross mark and O. Thispoint is taken as the origin of the polar coordinate system used todescribe mathematically the shaping of the rotor and stator plates andfor analyzing the operation of the combination. The curves describingthe outline of the stator plate are:

Where the letters indicate the radial distance to the outlines from theorigin along a radial line making an angle 0 with the horizontal linedesignated as the reference line. The third side of the stator plate 10is a straight radial line described by the simple equation:

The rotor plate 12 is outlined by a radial line, a circle of radius Rand a curve identical to that of the stator such that when the rotor hasturned through the angle,

0 Area= f r 016" The area of overlap is then:

let

from integral tables:

A= /;R sin a Consider next the area for values of a between ninety andone-hundred and eighty degrees. FIGURE 1b illustrates this region.Analagous to the prior calculation, the exposed area of the stator, A isreadily computed. The remaining area of overlap, A is then /2R -A a04-90 2 L Rate-]; [via sin (0+180a):l do

let

0 (-01) (sin y) 211111 (no-a =sin (a-90+180-a)-Sin (ISO-a) =1sin a.

e be

2 sin wt%) the quadrature of e. Let the voltage at the input to theamplifier be 2 The input impedance to the amplifier is very large sothat essentially no current flows to the amplifier input. The voltage, ethen, is determined by the current, I, flowing through the resistor andthe output voltage e thus:

Consider now that the capacitors C and C are of the design discussed inconnection with FIGURE 1 and that they are arranged to be operated bythe same shaft and located 90 apart.

Then:

e G sin ee -PG sin (a.%)e where G=Rjw e =Ge sin a. sin wt+ Ge Sil1(o.sin wte =Ge(sin a sin wt+cos oz cos wt) By analogy with Equations 1 and2 this is equivalent to:

e =Ge cos (wt-km) Equation 5 shows that the capacitive resolver whenoperated in connection with an amplifier as just described performs afunction which is equivalent to that performed by an electromechanicalresolver. These principles are further elaborated upon in the followingmaterial with respect to the descriptions of a single speed and atwo-speed capactive resolver.

FIGURES 3 and 4 illustrate a single speed capacitive resolver havingstator plates, 1-4, each of which is electrical-1y insulated from theothers, and a rotor plate 5 which is axially spaced from the statorplates to be capacitively associatey therewith. In FIGURE 3, the rotoris shown in the reference position. It is seen that each of the statorplates is of exactly the same design as studied earlier in connectionwith FIGURE 1. A

Stator plates 1 and 3 are connected in opposite polarity to thereference voltage, as shown. When the rotor 5 passes over stator 1, avoltage in phase with the reference voltage is impressed on the rotor.When the rotor passes over stator 3, a voltage 180 out of phase withsame reference voltage is impressed. This corresponds to the 180 phaseshift obtained in a standard resolver when the armature is rotated 180.The quadrature of the reference voltage is applied to plates 2 and 4 ina like manner, as shown in the figures. A single rotor plate 5 of thedesign already described is connected to the amplifier input thusforming the connected sides of C and C as described in connection withFIGURE 2.

FIGURE 4 illustrates this same single speed capacitive resolver with theshaft turned through an angle of about 45. As shown, the areas of plates'1 and 4 marked by horizontal lines are capacitively associated withrotor plate 5.

FIGURE 5:: shows the stator configuration of a two speed capacitiveresolver and FIGURE 5b, the rotor 0 to be used with this stator. The twospeed stator has eight insulated plates 21-28 disposed in circularsymmetry about a central axis. Here the odd number stators are connectedto the reference voltage in phase and out of phase by 180 alternately.The even numbered segments are connected similarly to the quadrature ofthis reference voltage. The equation of the concave edge of these statorsegments is:

Multispeed capacitive resolvers are made by applying the general formulafor the concave edge of the stator segments of:

r/R sin n;

where n=the speed of the capacitive resolver.

The value of n can be made arbitrarily large. Reduction to practice maybe accomplished by drawing the de- 6 sign for the rotor and stator partsto a very large scale and then photographically reducing the design. Thereduced photograph is then used to print an image on a metallic filmlaminated to a plastic sheet. By etching the resulting print, themultipolar stators and rotors can be made to great precision.

While the invention has been specifically described with reference toembodiments thereof, it is to be understood that much embodiments arenot to be construed as limiting the invention but are merelyillustrative. For a definition of the invention, reference should be hadto the following claims.

What is claimed is:

1. A capacitive resolver for producing electrical signals related inphase to the angular disposition of two relatively rotatable memberscomprising a rotor member and a stator member, one of the membersincluding four identical flat conductive plates which are symmetricallydisposed about an axis in coplanar fashion, each of said plates beingbounded by a straight edge of length R extending radially from saidaxis, an arcuate peripheral edge of radius R, and a concavely curvededge described by the equation =x/IZR sin wherein r is the radialdistance from the center of the arcuate edge and 0 is the angle measuredfrom said straight edge, a firs-t time varying voltage impressed acrossone diagonally opposite pair of plates, and a second time varyingvoltage in quadrature with the first volt-age impressed across the otherdiagonally opposite pair of plates, the other of the members including asingle conductive plate extending raidally from said axis and rotatablethereabout, said single plate being mounted by a straight radiallyextending edge of length R, an arcuate peripheral edge of radius 'R, anda convexly curved edge described by the equation 2R sin wherein r is theradial distance from the center of the last mentioned arcuate edge and 0is the angle measured from the last mentioned straight edge, said singleplate being axially spaced from the plates of said one member andcapacitively associated therewith whereby a voltage is induced on thesingle plate having a phase angle with respect to one of the timevarying voltages related to the angle of displacement of said singleplate with respect to said four plates.

2. A capacitive resolver as defined in claim 1 including a high negative.gain amplifier having its input connected with said single capacitiveelement, and a feedback resistor connected between the output and inputof the amplifier whereby the amplifier output voltage has a phase angle,with respect to the reference voltage, equal to the angle ofdisplacement of the rotor from its reference position.

3. A multispeed capacitive resolver comprising stator and rotor members,one of the members including 411 identical capacitive elements insulatedfrom each other and symmerically arranged about an axis in coplanarfashion with each element being contained within a sector of 360/4ndegrees, each of said identical capacitive elements being a flat platebounded by a straight edge of length R extending radially from saidaxis, an arcuate peripheral edge of radius R, and a concavely curvededge described by the equation 7 x ER sin Q 2 wherein r is the radialdistance from the center of the arcuate edge and 0 is the angle measuredfrom said straight edge, the other of the members including it identicalcapacitive elements electrically connected together and coplanarlyarranged about said axis in a circularly symmetrical pattern with eachelement being contained within a sector of 360/4n degrees Where n is anyinteger greater than unity, said single capacitive element being a flatplate bounded :by a straight edge of length R extending radially fromsaid axis, an arcuate peripheral edge of radius R, and a convexly curvededge descnibed by the equation wherein r is the radial distance from thecenter of the last mentioned arcuate edge and 0 is the angle measuredfrom the last mentioned straight edge, the elements of the stator androtor members being axially spaced and capacitively associated, a sourceof reference alternating voltage connected across adjacent odd numberedcapacitive elements of said one of the members, and a source ofquadrature alternating voltage connected across adjacent even numberedelements of said one of the members whereby the voltage induced on thecapacitive element of said other of the members has a phase angle withrespect to the reference voltage of n times the relative angle ofdisplacement of the element from a reference position.

References Cited by the Examiner UNITED STATES PATENTS 2,004,613 6/1935Meacham 317--254 2,330,822 10/ 1943 Fischer 17 844 2,48 0,187 8/ 1949Gamertsfelder 32151 2,527,215 -10/1950 Hahn 178-44 2,802,178 8/ 1957Shafer et a1 -3246 1 3,146,394 8/1964 Frisch 32393 JOHN F. COUCH,Primary Examiner.

LLOYD MCCOLLUM, MILTON O. HIRSH-FIELD,

Examiners.

A. D. PELLINEN, Assistant Examiner.

UNITED STATES PATENT OFFICE CERTIFICATE OF CORRECTION Patent No.3,265,960 August 9, 1966 Benjamin P. Blasingame It is hereby certifiedthat error appears in the above numbered pat ent requiring correctionand that the said Letters Patent should read as corrected below.

Column 4, line 26, for that portion of the equation reading 2A read 2Aline 64, for that portion of the equation on the right-hand side reading"+e read +e line 67, the equation should appear as shown below insteadof as in the patent:

e -Ke ,e--- K e lines 73 and 74, for that portion of the equationreading 1 read 1 2 Ke o Z 'K o o column 5, line 32, for "associatey"read associated column 6, line 9, for "much" read such -a Signed andsealed this 22nd day of August 1967.

(SEAL) Attest:

ERNEST W. SWIDER EDWARD J, BRENNER Attesting Officer Commissioner ofPatents

1. A CAPACITIVE RESOLVER FOR PRODUCING ELECTRICAL SIGNALS RELATED INPHASE TO THE ANGULAR DISPOSITION OF TWO RELATIVELY ROTATABLE MEMBERSCOMPRISING A ROTOR MEMBER AND A STATOR MEMBER, ONE OF THE MEMBERSINCLUDING FOUR IDENTICAL FLAT CONDUCTIVE PLATES WHICH ARE SYMMETRICALLYDISPOSED ABOUT AN AXIS IN COPLANAR FASHION, EACH OF SAID PLATES BEINGBOUNDED BY A STRAIGHT EDGE OF LENGTH R EXTENDING RADIALLY FROM SAIDAXIS, AN ARCUATE PERIPHERAL EDGE OF RADIUS R, AND A CONCAVELY CURVEDEDGE DESCRIBED BY THE EQUATION